Comparison of first aggregation and last aggregation in fuzzy group TOPSIS

Abstract

The Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), one of the major multi attribute decision making (MADM) techniques, ranks the alternatives according to their distances from the ideal and the negative ideal solution. In real evaluation and decision making problems, it is vital to involve several people and experts from different functional areas in decision making process. Also under many conditions, crisp data are inadequate to model real-life situations, since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Therefore aggregation of fuzzy concept, group decision making and TOPSIS methods that we denote “fuzzy group TOPSIS” is more practical than original TOPSIS. There are two approaches for aggregating values including relative importance of evaluation criteria with respect to the overall objective and rating of alternatives with respect to each criterion in fuzzy group TOPSIS: (1) First aggregation, (2) Last aggregation. In first aggregation approach weight of each criterion and rating of alternatives with respect to each criterion gained from decision makers are aggregated at first and TOPSIS method then apply to these aggregate values. In last aggregation approach weight of each criterion and rating of alternatives with respect to each criterion gained from decision makers are used in TOPSIS method directly. Distance of each alternative from the ideal and the negative ideal solution are calculated then aggregated for finding relative closeness of each alternative to the ideal solution. Two examples are presented to highlight the procedure of the proposed methods at the end of this paper. We want to test if variation in decision makers’ opinions is high, last aggregation method is more precise than first aggregation and vice versa when this variation is low, first aggregation method is as precise as last aggregation but faster than this method.